Question 808297
Let {{{ n }}} = number of nickels
Let {{{ d }}} = number of dimes
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(1) {{{ 5n + 10d = 415 }}} ( in cents )
(2) {{{ n + d = 52 }}}
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Multiply both sides of (2) by {{{ 5 }}} and
subtract (2) from (1)
(1) {{{ 5n + 10d = 415 }}}
(2) {{{ -5n - 5d = -260 }}}
{{{ 5d = 155 }}}
{{{ d = 31 }}}
and, since
(2) {{{ n + d = 52 }}}
(2) {{{ n = 21 }}}
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There are 21 nickels and 31 dimes
check:
(1) {{{ 5*21 + 10*31 = 415 }}} 
(1) {{{ 105 + 310 = 415 }}}
(1) {{{ 415 = 415 }}}
OK